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The number of points at which g(x)=1/(1+...

The number of points at which `g(x)=1/(1+2/(f(x)))` is not differentiable, where `f(x)=1/(1+1/x)` , is a. `1` b. `2` c. `3` d. `4`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=(1)/(1+(1)/(x))=(x)/(x+1)` is not differentiable at `x=0,-1.`
Also, `g(x)=(1)/(1+(2)/(f(x)))=(1)/(1+(2(x+1))/(x))=(x)/(3x+2)`
Thus, the point where g(x) is not differentiable are x = 0, `-1, -2//3`.
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